Robust and Efficient Fitting of Loss Models

We consider robust and efficient fitting of claim severity models whose parameters are estimated using the method of trimmed moments, which was recently introduced by Brazauskas, Jones, and Zitikis. In this article we take the “next” step by going beyond the theory and simulations. We address important issues that arise in practical application of the method. Specifically, we introduce two graphical diagnostic tools that can be used to choose the trimming proportions and hence help one to decide on the appropriate trade-off between robustness and efficiency. What is equally important, such tools are useful in model selection, for assessing the overall goodness of model fit, and for identification of outliers. Some insights about the choice between a “good” fit and an “even better” fit and its impact on risk evaluations are provided. Data analysis and illustrations are performed using real data that represent the total damage done by 827 fires in Norway for the year 1988.